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Unformatted text preview: Ch. 34 p. 1 CHAPTER 34 Lenses and Optical Instruments 1. ( a ) From the ray diagram, the object distance is about 3 & focal lengths, or 250 mm . O I F F ( b ) We find the object distance from (1/ d o ) + (1/ d i ) = 1/ f ; (1/ d o ) + (1/88.0 mm) = 1/65.0 mm, which gives d o = 249 mm = 24.9 cm . 2. To form a real image from a real object requires a converging lens . We find the focal length of the lens from (1/ d o ) + (1/ d i ) = 1/ f ; (1/285 cm) + (1/48.3 cm) = 1/ f , which gives f = + 41.3 cm . Because d i > 0, the image is real . 3. ( a ) The power of the lens is P = 1/ f = 1/0.275 m = 3.64 D, converging . ( b ) We find the focal length of the lens from P = 1/ f ; 6.25 D = 1/ f , which gives f = 0.160 m = 16.0 cm, diverging . 4. ( a ) We locate the image from (1/ d o ) + (1/ d i ) = 1/ f ; (1/18 cm) + (1/ d i ) = 1/24 cm, which gives d i = 72 cm. The negative sign means the image is 72 cm behind the lens (virtual). ( b ) We find the magnification from m = d i / d o = ( 72 cm)/(18 cm) = + 4.0 . 5. ( a ) Because the Sun is very far away, the image will be at the focal point. We find the size of the image from m = h i / h o = d i / d o ; h i /(1.4 10 6 km) = (28 mm)/(1.5 10 8 km), which gives h i = 0.26 mm . ( b ) For a 50 mm lens, we have h i /(1.4 10 6 km) = (50 mm)/(1.5 10 8 km), which gives h i = 0.47 mm . ( c ) For a 200 mm lens, we have h i /(1.4 10 6 km) = (200 mm)/(1.5 10 8 km), which gives h i = 1.9 mm . Ch. 34 p. 2 6. We find the object distance from the required magnification (which is negative for a real object and a real image): m = h i / h o = d i / d o ; (2.70 10 3 mm)/(36 mm) = (8.00 m)/ d o , which gives d o = 0.107 m. We find the focal length of the lens from (1/ d o ) + (1/ d i ) = 1/ f ; (1/0.107 m) + (1/8.00 m) = 1/ f , which gives f = 0.105 m = + 10.5 cm . 7. ( a ) We find the image distance from (1/ d o ) + (1/ d i ) = 1/ f ; (1/10.0 10 3 mm) + (1/ d i ) = 1/80 mm, which gives d i = 81 mm . ( b ) For an object distance of 3.0 m, we have (1/3.0 10 3 mm) + (1/ d i ) = 1/80 mm, which gives d i = 82 mm ....
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This note was uploaded on 04/03/2008 for the course PHYS 1C taught by Professor Whitten during the Winter '07 term at UCLA.
 Winter '07
 Whitten

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